to sum it up, the following things happened:
1. Conan's contract with NBC as host of Late Night was coming up in 2004, so NBC knew they didn't want to lose their second hottest late night show host, so they signed him a new deal with a promise, he gets the Tonight Show come 2009.
2. Jay Leno was meant to retire in 2009, when Conan was meant to take over.
3. Jay didn't want to retire, so pretty much, NBC was having to deal with the possibility of losing Leno instead, so they signed him on to a new deal to host a Primetime version of a late night talk show, the Jay Leno Show.
4. the transition happens in 2009, Leno's last show of the first tenure of the Tonight Show airs on Friday, May 29 and then the following Monday, June 1st, Conan's Tonight Show signs on, then the Jay Leno Show debuts at 10 PM ET on Monday, September 14.
5. then ratings became a issue as Leno's demo didn't migrate over the 10 PM ET time slot, the Conan fans didn't migrate well to the 11:35 PM ET and Conan's Tonight Show wasn't the show the fans of the Leno's version liked, and they didn't come back to Conan's Tonight Show. and fans of both shows felt the 2 shows were watered down versions of Conan's Late Night and Leno's Tonight Show, thus rating issues came to be known.
6. NBC wasn't happy with the ratings and neither was Leno and Conan or the Local stations as Leno's failure in primetime was cutting into late local news ratings and they didn't like Conan's Tonight Show being lead in by the local news.
7. NBC knowing that Leno flopped at 10 PM ET wanted to move him back to his old slot as "The Jay Leno Show" and air the show as a 30 minute show, which angered Conan as it would displace the Tonight Show into 12:05 AM ET (which would still be Tonight in the Central time zone) and he didn't want to have his show and late night & Carson Daily's Last Call bumped down by 30 minutes, a meeting was held between NBC network bosses, Conan and his producer Jeff Ross and then the next day, they were done with NBC after realizing they were getting screwed, they got their lawyers involved to sue NBC for breach of contract over broken promises.
8. the drama plays out in public, Leno was mocked by Jimmy Kimmel going as far as to troll Leno in a live via satellite interview where Jimmy was in his studios at the Hollywood Masonic Temple in Hollywood and Leno at NBC studios in Burbank, Letterman had Conan on, and even went as far as to say "Don't blame Leno" as it's not Jay or Conan's fault it was dumb network executives trying to keep both happy and did a poor job at it.
9. NBC Reaches a agreement with Conan's lawyers to release Conan out of his contract, thus officially ending the Conan O'Brien's Tonight Show run and instead of moving "The Jay Leno Show" to 11:35 PM ET, they canceled it and merged it into "The Tonight Show" franchise and Conan's predecessor became Conan's successor, Conan's last show was on Friday, January 22, 2010 and the last episode of "The Jay Leno Show" was Tuesday February 9th, as NBC's late night went on a Olympics break for the 2010 Winter Olympics.
10. Leno's second and final tenure as host of "The Tonight Show" begins on Monday, March 1st, after the Olympics ended, Conan was released from his contract and went on a comedy tour throughout 2010 and was placed on a gag order not to talk about his Tonight Show run, he wouldn't start a new show until November of that year (he had a non-compete clause that ended September 1st), and for the final week of shows on The Tonight Show, he couldn't legally have Howard Stern be a guest on his show due to Stern's own falling out with NBC over his time on the now defunct NBC Radio division's WNBC as well as Conan being awarded $45 Million Dollars along with the payment of his remainder of his contract. Conan would go on to sign on with TBS in the fall of 2010 debuting his new show "Conan" on Monday, November 8th.
11. The NBC executives responsible for this debacle lost their jobs when a regime changed happen shortly after, Conan was able to get a deal to allow his NBC years of video footage to be used by his new employer TBS, also he gain the ability to use his IP for Triumph The Insult Comic Dog character and returned to NBC TV for a cameo.
12. Leno retires from Late Night for good in 2014, Conan retires from late Night 2021 after trimming his show down to 30 minutes in 2019, with the intent to do more shows on HBOMax/Max in the near future but Covid Pandemic screwed things up then the Warner Brothers Discovery merger and Discovery+/HBOMax merger was completed in late May to form Max.
pretty much, letting Conan leave NBC much earlier or letting Leno leave in 2009 as planned would have been the best scenario where there is no "Jay Leno Show" and Conan's tenure would have lasted longer to the point he would have found his groove as host of the Tonight show.